This invention relates to a rigid mini-monolith structure which displays particular utility as a catalyst support, heat exchange media, and to a novel die construction for its formation. Such structures are generally relatively small and are usually formed by the extrusion of ceramic, cermet, glass, glass-ceramic, and metal powder or particulate material, and/or organic polymer or other suitable material from a die. Examples of similar structures which function as catalyst supports are shown in U.S. Pat. Nos. 4,054,702 issued to Lundsager et al, 4,328,130 issued to Kyan, and 4,510,261 issued to Pereira, all incorporated by reference. While apparently satisfactory for the function of a catalyst support, the structures shown in the Kyan and Pereira patents do not appear to maximize the available surface area on which the catalyst is placed for treatment of exhaust gases, for example. Further, neither they nor other prior disclosures teach how to maximize surface area while at the same time maximizing crushing strength of the structure.